Lateral Stability
Stability Dialog Box
Figure 1 Stability Dialog Box Showing the Beam Selection Tab
The potential for developing cracks due to additional tensile stress induced in a long prestressed concrete beam during lifting and transportation is a known problem. Another area of concern is the beam entering an unstable condition by rolling over along its longitudinal axis during transportation. This stability module in Precast/Prestressed Girder calculates the factor of safety against these undesirable conditions during lifting and transportation of long prestressed concrete beams under various support conditions. The program calculates the factors of safety against cracking and rollover, and stresses at critical points along the beam. The methodology follows the procedures outlined in PCI Journal articles by Dr. Robert Mast (see the References appendix).
The main features of this module are:
- Analyzes the behavior of precast beams hanging from lifting loops
- Analyzes the behavior of precast beams supported on truck and trailer
- Evaluates the wind effects on beams hanging from lifting loops or supported by truck and trailer
- Evaluates the effect of inclined cables used for hanging beams
- Includes the dynamic/impact effects during transportation
- Graphically shows the variation of factors of safety with the overhang or support distance from the end
- Computes factors of safety against crack initiation and complete failure for precast beams hanging from lifting loops
- Computes factors of safety against crack initiation and rollover for beams supported on a truck and trailer during transportation
According to AASHTO LRFD Art. 5.5.4.3, "Buckling of precast members during handling, transportation, and erection shall be investigated." This module addresses this issue with two support conditions for the precast beams:
Beam Hanging from Lifting Loops
Classical studies of lateral buckling of beams are based on the assumption that the beams are restrained from rotation at the supports. Buckling is caused by the middle part of the span twisting relative to the support, creating a sideways deflection.
The torsional stiffness of an I-beam varies as the cube of the thickness of the web and flanges. Concrete I-beams with relatively thick webs and flanges are stiffer in torsion. As a result, lateral buckling of the classic type is seldom critical in a concrete beam. However, when the supports have roll flexibility, the beams may roll sideways, producing lateral bending of the beam. This is the cause of most lateral stability problems involving long concrete I-beams.
When the beam is hanging from lifting loops, the maximum tilt angle at which the tensile stress in a corner of the top flange reaches out the modulus of rupture is found. Under that condition, the ratio of resisting moment to overturning moment is reported as the factor of safety against cracking. As the tilt angle increases, more and more cracks develop and the beam finally reaches the condition when it becomes unusable. Under that condition, the ratio of resisting moment to overturning moment is reported as factor of safety against failure.
Beam Supported on a Truck and Trailer
When a beam is supported on a truck and trailer, there is a tendency for the center of gravity of beam to roll about a roll axis. In such a case, the roll center is below the beam. Because the roll axis is beneath the center of gravity, the support must be capable of providing resistance to rotation. This resistance is expressed as an elastic rotational spring constant K-theta. K-theta may vary in the range of 3,000 to 6,000 kip-in per dual tire axle. For instance, a steer trailer with four dual and one single axle might be expected to have a roll stiffness of 4.5 * (3000 to 6000) = 13,500 to 27,000 kip-in per radian. The total K-theta for the rig is the sum of the stiffness of the truck and trailer. These values are based on a very limited number of measurements, so for critical shipments, it is strongly recommended that measurements be made of the roll stiffness of the actual vehicles to be used. See the References appendix for more information.
As in the case of the beam hanging from loops, a factor of safety against cracking is found as the ratio of resisting moment to overturning moment, when the first cracking occurs in the top flange of the beam supported on the truck and trailer. Again, this happens due to excessive rotation (tilt) of the beam about the roll axis. The factor of safety against rollover for the beam supported on truck and trailer is found through the ratio of resisting moment to overturning moment when the resisting moment offered by the truck and trailer is maximized. This maximum resisting moment of truck and trailer is based on the maximum distance of dual tires from the centerline of the truck and trailer system.
Wind forces on beams produce additional initial eccentricity due to the deflection caused by wind. Additionally, the wind load itself causes an overturning moment about the bottom of the bearing pads.
Beam Hanging from Loops Tab
The information on this tab is automatically read from the program, but allows for the modification of certain data for the purpose of the stability check process.
Figure 2 Beam Hanging from Loops Tab Data
Input parameters entered on this tab are as follows:
- Area (in2 or mm2): Cross sectional area of the beam.
- Depth (in or mm): Total height of the precast beam.
- Yb (in or mm): Centroid of concrete section above soffit.
- Concrete Strength (ksi or MPa): Strength of concrete at the time of lifting
- Concrete Density (pcf or kg/m3): Density of beam concrete
- Overall Length (ft or m): Total precast length of the beam
- Lateral Moment of inertia (in4 or mm4): Moment of inertia of the beam cross section about weak axis (for bending in horizontal plane)
- Vertical Moment of inertia (in4 or mm4): Moment of inertia of the beam cross-section about strong axis (for bending in vertical plane)
- Top Flange Width (in or mm): Width of beam top flange
- Modulus of Elasticity (ksi or MPa): Young's Modulus of the beam concrete
- Modulus of Rupture (ksi or MPa): Modulus of Rupture for the beam concrete
- Prestress Force (kips or N): Total prestress force induced by all strands
- Mid Height (in or mm): Height of strand CG at mid span of beam
- End Height (in or mm): Height of strand CG at end of beam
- Depress Point: Ration of location of depress point for draping to Overall Length of the beam
- Theta (degree): Angle of inclination of lifting looping with the horizontal (90 degree for vertical cable)
- Wind Pressure (psf or kPa): Horizontal wind pressure on beam
- Hanging Point Height (in or mm): Height of hanging point above the beam CG
- Overhang Distance (ft or m): Distance of lifting loop from beam end
- PCI Sweep Tolerance (in/in or mm/mm): Sweep tolerance used in the computation
- PCI Placement Tolerance (in or mm): Placement tolerance used in the computation
Other user interfaces on this screen are as follow:
- Inclined Cables: An inclination (other than vertical) of lifting cables can be specified by checking the box Lift using inclined cables and entering the value of angle inclination in degrees. For a perfectly vertical cable, the angle of inclination is assumed to be 90 degree (default).
- Wind Forces: Wind forces on beams produce additional initial eccentricity due to the deflection caused by wind. Additionally, the wind load itself causes an overturning moment about the bottom of the bearing pads. Specify the presence of wind force by checking the box Include wind force and entering a magnitude (as a pressure intensity acting horizontally on the beam).
- Strand Pattern: In the Strand Pattern section, you can modify total prestress force, heights of strand CG at mid span and at beam end and the location of depress point for draping. If the Straight option is selected, CG height at beam end and the location of depress point for draping are not available. In order for these two input parameters to be active, the Draped option should be selected.
- Calculate: Click the Calculate button for a short list of important results to appear in the adjacent text box. This list consists such results as factors of safety, beam stresses at lifting points and at mid-span (or at depress point), etc.
- Show Results: Check the results by clicking the Show Results button. This activates the Results screen which contains all input data as well as most intermediate data computed.
- Graph: Click the Graph button to display the Graph screen, showing a plot of various lift point locations and the related factors of safety. The screen displays graphically the relationship between the factor of safety and overhang distance. Depending on the option selected, the graph will display the factor of safety against cracking or against failure or against rollover. To change the plot distance, enter its value in the adjacent edit box and click the Redraw button. Click the Print button to get a hard copy of the graph display from your printer. Click the Close button to close this screen and go back to the originating screen.
Figure 3 Results Dialog Box Showing Computed Input Data
Figure 4 Graph Dialog Box Showing Plots of Various Lift Point Locations and Related Safety Factors
Beam on Truck and Trailer Tab
The information on this tab is automatically read from the program, but allows for the modification of certain data for the purpose of the stability check process.
Input parameters entered on this tab are as follows:
- K-theta (k-in/radian or N-mm): Sum of rotational spring constants for truck and trailer support
- Height of beam CG above road (in or mm): Distance of beam CG above road
- Height of roll axis above road (in or mm): Distance of roll axis above road
- Superelevation angle (radians): Superelevation angle of the road surface
- Z-max (in or mm): Centerline (CL) of vehicle to CL of dual tires distance
- Off-Center Tolerance (in or mm): Tolerance to compute initial eccentricity of beam with respect to the center of truck and trailer
- Bottom Flange Width (in or mm): Width of bottom flange of beam
- Wind Pressure (psf or kPa): Horizontal wind pressure on beam
- Overhang distance (ft or m): Measured from bean end to support point
- Impact Factor: A factor to consider the dynamic effects
Other user interfaces on this screen are:
- Beam Properties: Under the Beam Properties section, select either the Use hanging beam properties or Use different beam properties option. Click the Edit button to edit the strand pattern if the second option is chosen. If you have selected the Use hanging beam properties option, you will not be able to edit the strand pattern here.
- Wind Forces: Wind forces on beams produce additional initial eccentricity due to the deflection caused by wind. Additionally, the wind load itself causes an overturning moment about the bottom of the bearing pads. Specify the presence of wind force by checking the box Include wind force and entering a magnitude (as a pressure intensity acting horizontally on the beam).
- Calculate: Click the Calculate button for a short list of important results to appear in the adjacent text box. This list consists such results as factors of safety, beam stresses at lifting points and at mid-span (or at depress point), etc.
Figure 5 Beam on Truck and Trailer Tab Showing Supported Beam